Problem: Solve for $x$ and $y$ using elimination. ${-2x+6y = 18}$ ${2x+5y = 26}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the top and bottom equations together. $11y = 44$ $\dfrac{11y}{{11}} = \dfrac{44}{{11}}$ ${y = 4}$ Now that you know ${y = 4}$ , plug it back into $\thinspace {-2x+6y = 18}\thinspace$ to find $x$ ${-2x + 6}{(4)}{= 18}$ $-2x+24 = 18$ $-2x+24{-24} = 18{-24}$ $-2x = -6$ $\dfrac{-2x}{{-2}} = \dfrac{-6}{{-2}}$ ${x = 3}$ You can also plug ${y = 4}$ into $\thinspace {2x+5y = 26}\thinspace$ and get the same answer for $x$ : ${2x + 5}{(4)}{= 26}$ ${x = 3}$